Analysis & PDE

  • Anal. PDE
  • Volume 10, Number 2 (2017), 323-350.

Operators of subprincipal type

Nils Dencker

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Abstract

In this paper we consider the solvability of pseudodifferential operators when the principal symbol vanishes of at least second order at a nonradial involutive manifold Σ2. We shall assume that the subprincipal symbol is of principal type with Hamilton vector field tangent to Σ2 at the characteristics, but transversal to the symplectic leaves of Σ2. We shall also assume that the subprincipal symbol is essentially constant on the leaves of Σ2 and does not satisfying the Nirenberg–Trèves condition (Ψ) on  Σ2. In the case when the sign change is of infinite order, we also need a condition on the rate of vanishing of both the Hessian of the principal symbol and the complex part of the gradient of the subprincipal symbol compared with the subprincipal symbol. Under these conditions, we prove that P is not solvable.

Article information

Source
Anal. PDE, Volume 10, Number 2 (2017), 323-350.

Dates
Received: 23 November 2015
Revised: 18 September 2016
Accepted: 1 November 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1510843424

Digital Object Identifier
doi:10.2140/apde.2017.10.323

Mathematical Reviews number (MathSciNet)
MR3619872

Zentralblatt MATH identifier
06693359

Subjects
Primary: 35S05: Pseudodifferential operators
Secondary: 35A01: Existence problems: global existence, local existence, non-existence 58J40: Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx] 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx]

Keywords
solvability pseudodifferential operator subprincipal symbol

Citation

Dencker, Nils. Operators of subprincipal type. Anal. PDE 10 (2017), no. 2, 323--350. doi:10.2140/apde.2017.10.323. https://projecteuclid.org/euclid.apde/1510843424


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